In a fuel cell system, a fuel cell of a solid polymer type is mounted in which a solid polymer membrane having a proton conductivity is applied to an electrolyte layer. As a method for detecting an abnormality generated in such a fuel cell, a method is known in which the impedance of the fuel cell when applying an alternate current having a specific frequency (hereinafter referred to as the impedance having the specific frequency) is measured to detect the abnormality based on the measurement result (e.g., see Patent Document 1).    Patent Document 1: Japanese Patent Application Laid-Open No. 2002-367650